Vacuum Fluctuations and the Renormalized Stress-Energy Tensor on a Cone with Arbitrary Boundary Conditions
Abstract
We analyze the vacuum fluctuations and the stress-energy tensor of a scalar field of mass in a conical spacetime, where the topological singularity at the apex requires boundary conditions for the field equation. The necessity of boundary conditions was established by Kay and Studer in the early 1990s, but the consequences of their arbitrariness, represented here by a parameter , for renormalized observables have not been examined. While for stability is achieved only under Dirichlet boundary conditions, for the field is stable and a localized mode emerges. This mode admits a natural interpretation as a covariant model of an extended particle detector, which allows us to investigate how such detectors modify the local vacuum structure. In this framework, the renormalized stress-energy tensor offers a natural way to quantify the influence of the detector on the surrounding spacetime.
Keywords
Cite
@article{arxiv.2509.20231,
title = {Vacuum Fluctuations and the Renormalized Stress-Energy Tensor on a Cone with Arbitrary Boundary Conditions},
author = {João Paulo M. Pitelli and Ricardo A. Mosna and Victor Hugo M. Ramos and João C. A. Barata},
journal= {arXiv preprint arXiv:2509.20231},
year = {2025}
}